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Subsequence sums of zero-sum free sequences over finite abelian groups

Volume 140 / 2015

Yongke Qu, Xingwu Xia, Lin Xue, Qinghai Zhong Colloquium Mathematicum 140 (2015), 119-127 MSC: Primary 11B50; Secondary 11P99. DOI: 10.4064/cm140-1-10

Abstract

Let $G$ be a finite abelian group of rank $r$ and let $X$ be a zero-sum free sequence over $G$ whose support $\mathrm {supp}(X)$ generates $G$. In 2009, Pixton proved that $|\varSigma (X)|\geq 2^{r-1}(|X|-r+2)-1$ for $r \le 3$. We show that this result also holds for abelian groups $G$ of rank $4$ if the smallest prime $p$ dividing $|G|$ satisfies $p\geq 13$.

Authors

  • Yongke QuDepartment of Mathematics
    Luoyang Normal University
    Luoyang 471022, P.R. China
    e-mail
  • Xingwu XiaDepartment of Mathematics
    Luoyang Normal University
    Luoyang 471022, P.R. China
    e-mail
  • Lin XueDepartment of Mathematics
    Luoyang Normal University
    Luoyang 471022, P.R. China
    e-mail
  • Qinghai ZhongUniversity of Graz
    Institute for Mathematics and Scientific Computing
    Heinrichstraße 36
    8010 Graz, Austria
    e-mail

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